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Some real-world decision-making problems require making probabilisticforecasts over multiple steps at once. However, methods for probabilisticforecasting may fail to capture correlations in the underlying time-series thatexist over long time horizons as errors accumulate. One such application iswith resource scheduling under uncertainty in a grid environment, whichrequires forecasting electricity demand that is inherently noisy, but oftencyclic. In this paper, we introduce the conditional approximate normalizingflow (CANF) to make probabilistic multi-step time-series forecasts whencorrelations are present over long time horizons. We first demonstrate ourmethod's efficacy on estimating the density of a toy distribution, finding thatCANF improves the KL divergence by one-third compared to that of a Gaussianmixture model while still being amenable to explicit conditioning. We then usea publicly available household electricity consumption dataset to showcase theeffectiveness of CANF on joint probabilistic multi-step forecasting. Empiricalresults show that conditional approximate normalizing flows outperform othermethods in terms of multi-step forecast accuracy and lead to up to 10x betterscheduling decisions. Our implementation is available athttps://github.com/sisl/JointDemandForecasting.

Conditional Approximate Normalizing Flows for Joint Multi-Step Probabilistic Forecasting with Application to Electricity Demand